Chapter 2 - ADD
A cumulative frequency distribution
shows the number of observations less than each class upper limit
Suppose a frequency distribution has the following consecutive classes: $20 up to $30 $30 up to $40 $40 up to $50 What is the class midpoint for the first class?
$25
Which of the following features is an advantage that the frequency polygon has over the histogram?
It can directly compare two or more frequency distributions.
Which of the following are true regarding the class midpoint? Select all that apply.
It is halfway between the lower limits of two consecutive classes. It is halfway between the upper limits of two consecutive classes. It best represents the values in a class.
Which of the following is an advantage of a frequency polygon over a histogram? Multiple choice question. It depicts each class as a rectangle, with the height representing the number of observations. A histogram can compare two or more distributions It shows class midpoints as points on a polygon.
It shows class midpoints as points on a polygon
Which of the following is not a characteristic of frequency distribution?
It summarizes qualitative data.
A frequency polygon shows the shape of a distribution and is similar to: Multiple choice question. a frequency table a bar chart a pie chart a histogram
a histogram
Which two of the following practices is commonly used in setting class limits for frequency distribution?
Rounding the class interval up Placing "excess" interval width equally in the two tails of the distribution
Which of the following would be a use of a frequency table? Select all that apply.
State of residence of students in a business statistics course Majors of students in a business statistics course Gender of students in a business statistics course
Which of the following is a feature of relative frequency distribution?
The sum of the relative frequencies must be (assuming no rounding errors).
In a marketing study, 100 consumers were asked to select the best digital music player from the iPod Touch, Sony Walkman, and Zune HD. To summarize the consumer responses with a frequency table, how many classes would the frequency table have?
There are 3 music players given in the question, so in the frequency table, there should be three classes to capture the consumer responses. Hence, the number of classes is 3.
A set of data consists of 38 observations. How many classes would you recommend for the frequency distribution?
Use "2 to the k rule:" 2(to the 5th)=32 32 is less than 38, so 5 classes are not enough Try the next highest number: 2(to the 6th)=64 64 is greater than 38, so the recommended number of classes is 6.
b. Suppose that 1,000 graduates will start a new job shortly after graduation. Estimate the number of graduates whose first contact for employment occurred through networking and other connections. c. Would it be reasonable to conclude that about 90% of job placements were made through networking, connections, and job posting websites?
b. To estimate the number of students receiving a job through networking, multiply 70% by 1,000: Estimated job by networking= 0.7 x 1000=700 It is estimated that 700 students will receive their jobs from networking. c. The proportion of jobs through website is 20%, through networking is 70%. Assuming that students are only allowed to pick one choice for how they receive their jobs, then 90% of students receive jobs thought network and website.
In a frequency polygon, the points are plotted at the intersection of the class frequencies and the:
class midpoints
The number of observations in each class is called the class _____.
frequency
In using the "2 to the k rule" to determine the number of classes for a frequency distribution, what is the meaning of the variable k?
k is the smallest number of classes such that 2 (to the k) is greater than the number of observations.
A useful way to determine the number of classes (k) in a frequency distribution of n items is the "2 to the k rule." Which of the following correctly describes this rule?
k is the smallest number such that 2(to the k)>n
In the histogram shown, how many vehicles were sold for a profit less than $1,400?
42
In the cumulative frequency polygon shown, about how many observations are there between a value of 200 and 250?
50, you must subtract the observations for 200 from the observations for 250
Place the following steps used in construction a frequency distribution into correct order.
Decide on the number of classes Determine class width Set individual class limits Tally the number of observations in each class
Suppose the cumulative frequency distribution is used to summarize n observations. The cumulative frequency for the last class will always be
Equal to n
Suppose that the miles per gallon for 80 cars is summarized in a frequency distribution. Below is a part of the distribution. What would the relative frequency be for the class "20 up to 24?" MPG Frequency 16 up to 20 10 20 up to 24 16
0.20 , 16/80=0.20 Relative frequency is calculated as the class frequency divided by the total number of cars. For the "20 up to 24" class, that would be (16/80) = 0.2.
A business statistics instructor teaches a class with 83 students. Suppose he would like to create a frequency distribution to summarize their 83 final exam scores. Using the "2 to the k rule," how many classes should be used?
7 is the smallest value of k that makes 2(to the k power) > n 2(to the 6th power) = 64 2(to the 7th power) = 128 128>83, so the answer is 6
Which of the following are characteristics of bar charts? Select all that apply.
Bar charts are used for qualitative data There should be gaps between bars Plotted rectangles should be the same width
Which of the following is not a useful practice in setting individual class limits for a frequency distribution? Multiple choice question. Round the class interval up to get a convenient class size. Excluding outliers that cause the interval to be too wide. Set clear limits so an observation will fit only one class. Place excess interval space equally in the two tails of the distribution.
Excluding outliers that cause the interval to be too wide. Reason: It is not sound practice to exclude data because it is inconvenient
Which of the following graphs are used to summarize quantitative data? Select all that apply.
Histogram Frequency Polygon
A small-business consultant is investigating the performance of several companies. The fourth-quarter sales for last year (in thousands of dollars) for the selected companies were: Identify a bar chart that compares the fourth-quarter sales of these corporations.
Maxwell clearly has the highest fourth-quarter sales from last year with $24,612,000, with is 60.4% of the total revenue from all six companies. They made more than twice than the second highest earner, Long Bay. Below Long Bay is J&R. These three companies ranked the highest out of the six in the fourth-quarter earnings last year. Mizell and Mancell did not fare so well, earning just 2% of the total revenue from all six companies. Hoden was also on the low end, coming in between J&R and Mancell.
The level of measurement required for qualitative variable are either nominal or ordinal. Interval and ratio scale measurements for qualitative variable are not appropriate because they both require that the magnitude of the difference between two variables is constant; however, the magnitude between two different qualitative variables cannot be determined. Qualitative variable?
Nominal and Ordinal
Which of the following is true about pie charts?
The area of a slice for a class relative to the whole pie should match its relative frequency.
Relative frequencies are
The fraction or percentage of observations in each class interval.
Which is the following features is not part of a histogram?
The frequency of occurrence of a nominal variable.
Which of the following features is not part of a histogram? Multiple choice question. Adjacent bars whose height represents a number or fraction. The frequency of occurrence of data within classes. The frequency of occurrence of a nominal variable. Quantitative data divided into classes.
The frequency of occurrence of a nominal variable. bien danh nghia Reason: Histograms are used to display properties of quantitative variables. (interval or ratio level)
Which one of the following is true regarding raw data?
Raw data are simply a listing of data before summarizing it.
A business statistics course has 2 accounting majors, 4 finance majors, 6 marketing majors, and 8 insurance majors. Which one of the following is true if a pie chart was constructed to depict majors of students?
The marketing slice would be three times as big as the accounting slice.
- The sum of the relative frequencies must be less than 1. incorrect Reason: - The sum of the relative frequencies is always 1. No two classes can have the same relative frequency. Reason: - If two classes have the same frequency, then they will have the same relative frequency. - The relative frequency is found by dividing the class frequencies by the total number of observations. - The sum of the relative frequencies is equal to the number of observations. Reason: The sum of the relative frequencies is always 1.
The relative frequency is found by dividing the class frequencies by the total number of observations.
Which of the following operations is true regarding relative frequency distributions?
The relative frequency is found by dividing the class frequencies by the total number of observations.
Which of the following can be observed from a histogram? Multiple select question. - The shape of the distribution. correct - The relationship between two variables. (Reason: A histogram only looks at one variable.) - The approximate number of observations. correct -The spread of the data. correct The concentration of the data.
- The shape of the distribution. - The approximate number of observations. - The spread of the data. - The concentration of the data.
In the cumulative frequency polygon shown, about how many observations are there between a value of 100 and 150?
25, to get this amount, you must subtract the cumulative frequency for 100 from that for 150
Given below are the data for blood types: A B B AB O O O B AB B A B 0 O O A O A A 0 A B B 0 AB Which is the frequency for blood type AB?
3 correct Reason: The blood type AB occurs three times.
Suppose a frequency distribution has the following consecutive classes: $20 up to $30 $30 up to $40 $40 up to $50 What is the class midpoint for the first class? $20 $30 $25 $10
50/2=25
Suppose you are trying to summarize a data set a maximum value of 70 and a minimum value of 1. If you have decided to use seven classes, which one of the following would be a reasonable class interval?
70-1=69; 69/7=9.9, closest is 10
Describe the similarities and differences between a frequency table and a frequency distribution. Be sure to include which requires qualitative data and which requires quantitative data.
A frequency table calls for qualitative data. A frequency distribution involves quantitative data
A set of data consists of 45 observations between $0 and $29. a. How many classes would you recommend for the frequency distribution? b. What class interval would you recommend? (Round your answer to the nearest whole number.)
First, determine number of classes using "2 to the k rule:" 2(to the 5)=32 32 is less than 45, so 5 classes are not enough Try the next highest number: 2(to the 6th)=64 64 is greater than 45, so the recommended number of classes is 6. The class interval is given by: i(greater than or equal to)H-L over (divided by) k Where i is the class interval, H is the highest observed value, L is the lowest observed value, and k is the number of classes Calculate class interval: $29-$0 divided by 6=$4.38 Round up to get the class interval of $5
To divide data with a high value of H and a low value of L into k classes, the class interval must be:
In most instances, this value will be fractional and the number of classes should be an integer. When this calculation results in an integer, the limit must be increased to include all observations.
Two thousand frequent business travelers were asked which Midwestern city they prefer: Indianapolis, Saint Louis, Chicago, or Milwaukee. One hundred liked Indianapolis best, 450 liked Saint Louis, 1,300 liked Chicago, and the remainder preferred Milwaukee. Prepare a frequency table and a relative frequency table to summarize this information. (Round "Relative Frequency" answers to 3 decimal places.)
Indianapolis 100 (frequency)/2000 = 0.05(Relative Frequency) St Louis 450/2000= 0.225 Chicago 1300/2000=0.65 Milwaukee 150/2000 = 0.075
The level of measurement required for qualitative variable are either nominal or ordinal. Interval and ratio scale measurements for qualitative variable are not appropriate because they both require that the magnitude of the difference between two variables is constant; however, the magnitude between two different qualitative variables cannot be determined. Quantitative variables?
Interval and Ratio
